Representations of solutions of Lindblad equations by randomized Feynman formulas

Abstract

Representations of solutions of Lindblad equations by randomized Feynman integrals over trajectories are obtained by averaging similar representations for solutions of stochastic Schrödinger equations (Schrödinger–Belavkin equations). An approach based on the application of Chernoff’s theorem is applied. First, (randomized) Feynman formulas approximating Feynman path integrals are obtained; these formulas contain integrals over finite Cartesian powers of the space of values of the functions over which the Feynman integrals are taken.